Theorems · Theorem · number theory
LSeries.convolution_def
∀ {R : Type u_1} [inst : Semiring R] (f g : ℕ → R),
LSeries.convolution f g = fun n => ∑ p ∈ n.divisorsAntidiagonal, f p.1 * g p.2- Defined in
- Mathlib.NumberTheory.LSeries.Convolution
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- mul_iteproof · cited by 159
- ite_mulproof · cited by 83
- Nat.divisorsAntidiagonalstatement and proof · cited by 61
- LSeries.convolutionstatement · cited by 18
- Nat.ne_zero_of_mem_divisorsAntidiagonalproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- DirichletCharacter.mul_convolution_distribproof · cited by 2
- LSeries.term_convolutionproof · cited by 1
- ArithmeticFunction.convolution_vonMangoldt_zetaproof · cited by 1
- LSeries.convolution_map_zeroproof · cited by 0